Problem

Verify that the measure of a vertex angle in a regular polygon is (n − 2)180°/n (Theorem 2...

Verify that the measure of a vertex angle in a regular polygon is (n − 2)180°/n (Theorem 2.3), by completing the given table as follows: (i) Sketch regular polygons with four, five, six, and more sides, and (ii) divide each polygon into triangles by drawing all possible diagonals from one vertex. Use inductive reasoning to develop the formula given in Theorem 2.3.

Number of Sides and Angles in a Polygon	Number of Triangles into Which the Polygon Can Be Divided	Sum of Angle Measures in the Polygon	Measure of One Angle in the Polygon
3	1	180°
4	2	2(180°) = 360°
5
6
8
10
n